Question

Based only on the information given in the diagram, it is guaranteed that JKL WXY

Answer 1

Step-by-step explanation

Two figures are similar when they have the same shape. In the case of polygons this means that two polygons are similar when they have the same internal angles. Then if triangles JKL and WXY are similar the following equalities must be met:

`\begin{gathered} \angle J=\angle W \\ \angle K=\angle X \\ \angle L=\angle Y \end{gathered}`

Angles X and K are equal because we know that their measures are 90°. We still need to find the measures of L and W and see if they are 63° and 27° respectively. If that's the case then the triangles are similar.

Remember that the sum of the three internal angles of a triangle is equal to 180°. Then for triangle JKL we have the following equation:

`\begin{gathered} \angle J+\angle K+\angle L=180 \\ 27+90+\angle L=180 \\ 117+\angle L=180 \end{gathered}`

We can subtract 117 from both sides:

Then for triangle WXY we have:

`\begin{gathered} \angle W+\angle X+\angle Y=180 \\ \angle W+90+63=180 \\ \angle W+153=180 \end{gathered}`

Then we substract 153 from both sides:

So we've found that:

`\begin{gathered} \angle J=\angle W=27^(\circ) \\ \angle L=\angle Y=63^(\circ) \\ \angle K=\angle X=90^(\circ) \end{gathered}`

Answer

They have the same internal angles so they are similar triangles. Then the answer is option A, True.